Question

The moment $p$(in $kgm{s}^{-1}$) of a particle is varying with time $t$(in $s$) as $p=2+3t^2$. The force acting on the particle at $t=3s$ will be

• A. $9N$
• B. $54N$
• C. $18N$
• D. $15N$

Answer 1

The correct option is C

$18N$

Step 1: Given data

Momentum, $p=2+3t^2$

We have to find force on the particle at $t=3s$

Step 2: Formula used and calculation

We know,

$$\begin{gathered} F=\frac{dp}{dt} \\ \Rightarrow F=\frac{d(2+3t^2)}{dt} \\ \Rightarrow F=6t \end{gathered}$$

since, $t=3s$

$$\begin{gathered} \because F=6\times 3 \\ \Rightarrow F=18N \end{gathered}$$

$\because$ Force on the particle at $t=3s$ is $18N$

Option C is correct